Question

Describe Sampling and samling distributions in business statistics in 175 words please type response.

Answer 1

sampling and sampling distribution in business statistics:

In statistics, sampling distributions are the probability distributions of any given statistic based on a random sample, and are important because they provide a major simplification on the route to statistical inference they allow analytical considerations to be based on the sampling distribution of a statistic, rather than on the joint probability distribution of all the individual sample values.

Regression analysis is a statistical tool used for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another — the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate.

how sampling distribution is used in business statistics is explained below

Regression analysis is used to estimate the strength and the direction of the relationship between two linearly related variables: X and Y. X is the “independent” variable and Y is the “dependent” variable.

The two basic types of regression analysis are:

• Simple regression analysis: Used to estimate the relationship between a dependent variable and a single independent variable; for example, the relationship between crop yields and rainfall.

• Multiple regression analysis: Used to estimate the relationship between a dependent variable and two or more independent variables; for example, the relationship between the salaries of employees and their experience and education.

  Multiple regression analysis introduces several additional complexities but may produce more realistic results than simple regression analysis.

• An estimated regression equation may be used for a wide variety of business applications, such as:

• Measuring the impact on a corporation’s profits of an increase in profits

• Understanding how sensitive a corporation’s sales are to changes in advertising expenditure

• Seeing how a stock price is affected by changes in interest rates

• next procedure in business statistics is hypothesis testing: refers to the process of choosing between competing hypotheses about a probability distribution, based on observed data from the distribution. It’s a core topic and a fundamental part of the language of statistics.

  Hypothesis testing is a six-step procedure:

      1.    Null hypothesis

      2.    Alternative hypothesis

      3.    Level of significance

      4.    Test statistic

      5.    Critical value(s)

      6.    Decision rule

  The null hypothesis is a statement that’s assumed to be true unless there’s strong contradictory evidence. The alternative hypothesis is a statement that will be accepted in place of the null hypothesis if it is rejected.

  The level of significance is chosen to control the probability of a “Type I” error; this is the error that results when the null hypothesis is erroneously rejected.

  The test statistic and critical values are used to determine if the null hypothesis should be rejected. The decision rule that is followed is that an “extreme” test statistic results in rejection of the null hypothesis. Here, an extreme test statistic is one that lies outside the bounds of the critical value or values.

• Random Variables and Probability Distributions in Business Statistics:

  Random variables and probability distributions are two of the most important concepts in statistics. A random variable assigns unique numerical values to the outcomes of a random experiment; this is a process that generates uncertain outcomes. A probability distributionassigns probabilities to each possible value of a random variable.

  The two basic types of probability distributions are discrete and continuous. A discrete probability distribution can only assume a finite number of different values.

  Examples of discrete distributions include:

• Binomial

• Geometric

• Poisson

• A continuous probability distribution can assume an infinite number of different values. Examples of continuous distributions are:

• Uniform

• Normal

• Student’s t-test

• Chi-square-test

• F-test